Dislocations in a layered elastic medium with applications to fault detection

Andrea Aspri, Elena Beretta, Anna L. Mazzucato

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a model for elastic dislocations in geophysics. We model a portion of the Earth's crust as a bounded, inhomogeneous elastic body with a buried fault surface, along which slip occurs. We prove well-posedness of the resulting mixed-boundary-value-transmission problem, assuming only bounded elastic moduli. We establish uniqueness in the inverse problem of determining the fault surface and the slip from a unique measurement of the displacement on an open patch at the surface, assuming in addition that the Earth's crust is an isotropic, layered medium with Lamé coefficients piecewise Lipschitz on a known partition and that the fault surface is a graph with respect to an arbitrary coordinate system. These results substantially extend those of the authors in {Arch. Ration. Mech. Anal.} {\bf 263} (2020), n. 1, 71--111.
Original languageEnglish (US)
JournalJournal of the European Mathematical Society
StateAccepted/In press - 2021

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